Select overlaping vertices from vertex groups
Deselect all the vertices, with A.
Select the first vertex group with the Select button under the vertex group list in the properties window.

Invert the selecting by pressing CtrlI.
Hide those vertices, with H.
Select the second vertex group (same way as in step 2).


Any vertices that are now selected are in both vertex groups.
After doing what you want with the double grouped vertices, you can show the whole mesh again by pressing AltH.

Animated gif showing first the two vertex groups, then how to find double grouped vertices, using the procedure listed above.